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How to derive pythagorean identity?

  1. Jul 5, 2007 #1
    I got some precalc review to prepare for calc, and after hours of doing the packet, I'm on the last problem set....but it's all about derivatives which we never touched on last year.

    1. The problem statement, all variables and given/known data
    I'm supposed to derive sin^2 + cos^2 = 1

    2. Relevant equations
    It says to use cos 0 =1, cos (x+y) = cos x cos y - sin x sin y, but I have no idea how to use these.

    please help! I'm absolutely clueless at math :frown:
  2. jcsd
  3. Jul 5, 2007 #2


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    All you need to do is choose y so that x+y = 0 and thus cos (x+y) = 1 and plug your values into the right hand side of the equation you're given. You will also need to know about cos being an even function and sin being an odd function.
  4. Jul 5, 2007 #3
    Thanks! I got it
  5. Jul 5, 2007 #4


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    Its not the best derivation of the result because it leaves you wondering what Pythagoras has to do with it. Its best to derive this result from the unit circle where the x coordinate is given by cos(x) and the y coordinate by sin (x) then it becomes immediately apparent where Pythagoras comes in.
  6. Jul 5, 2007 #5
    That interseting because i just derived pythagoras c^2=a^2+b^2 formula from an ellipse, very enlightening.
    Last edited: Jul 5, 2007
  7. Aug 6, 2009 #6
    sorry but can anyone please explain it to me again? i dont understand why you have to choose a value for y and not x and i dont see how even/odd functions will be used
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